Quantum information technology has gained tremendous momentum in the research arena over the past decade and its potential impact on the future was realised in South Africa when the Quantum Research Group at UKZN received a substantial amount of funding from the Innovation Fund to set up a Centre for Quantum Technologies and to develop a quantum key distribution system. One of the ultimate goals of quantum technology is to produce a completely self-sustained quantum computer. Quantum computers based on logic quantum gates are able to perform certain computational tasks more efficiently than classical computers. However, there are still technological shortcomings with respect to the realisation of quantum gates, the building blocks of the quantum computer.
One of the novel and most promising candidates in realising quantum gates are double-optical lattices, periodic atom structures created by atom-photon interactions. The double-optical lattice structure was first implemented by Prof A. Kastberg and his research team (Umea, Sweden). The Quantum Research Group at UKZN is involved in collaborations with this research team and much progress has been made in the development of a quantum model that can be used to simulate quantum state manipulation of atoms or de-coherence in this lattice structure. It is vital to be able to simulate the dynamics of the atoms in the construction of these quantum gates. The numerical simulation of this model is based on Monte Carlo Wave Function techniques, renowned as an efficient numerical tool, for their and requires the diagonalization of matrices of 10 000 x 10 000 for a complete description of the dynamics. With these techniques and ensemble of stochastic state vectors are propagated in the open system's space so that the reduced-density matrix is recovered through an appropriate ensemble average. Unravellings of time-local non-Markovian quantum master equations in a doubled Hilbert space obtained by time-convolutionless projection operator technique allow for efficient Monte Carlo algorithms.
A generalisation of the Lindblad theory on the regime of highly non-Markovian quantum process in structured environments has been developed by H.P. Breuer, with whom the UKZN Quantum Research Group collaborates in research efforts. This research intends to investigate realistic quantum optical and spintronic devices that exhibit non-Markovian behaviour by using recently-developed algorithms. Exact Monte Carlo methods have been developed for the representation of the non-Markovian dynamics of open quantum systems. These techniques lead to an exact solution of the Von Neumann equation of the total system and they have been shown to be successful in studies of simple-spin models for de-coherence.